Question

Решить систему уравнений
x=2y

log1/3(2y+x)+log1/3(x-y+1)=log3(1/y+1)

Answer 1

x=2y

log(1/3)(2y+x)+log(1/3)(x-y+1)=log(3) 1/(y+1)
подставляем

log(1/3)(2y+2y)+log(1/3)(2y-y+1)=log(1/3) (y+1)
log(1/3) 4y + log(1/3)(y+1)=log(1/3) (y+1)
log(1/3) 4y = 0
4y = 1
y = 1/4
x = 1/2
проверим
log(1/3)(2*1/4+1/2)+log(1/3)(1/2-1/4+1)=log(3) 1/(1/4+1)
log(1/3)(1)+ log(1/3)(5/4)=log(3) 4/5
0+ log(1/3)(5/4)=log(1/3) 5/4 да